Example data analysts

Mushroom growth data

Here, we are looking at growth rates for two species of commercial mushrooms: Pleurotus ostreotus and P. cornucopiae.

Let’s take a quick look at the data structure:

Species Light Nitrogen Humidity Temperature GrowthRate
P.ostreotus 0 0 Low 20 23.924
P.ostreotus 10 0 Low 20 34.132
P.ostreotus 20 0 Low 20 134.782
P.ostreotus 0 5 Low 20 44.516
P.ostreotus 10 5 Low 20 44.252

We have a few variables that were measured, and the outcome of growth rate is in g/day. The independent variables were…

## [1] "Species"     "Light"       "Nitrogen"    "Humidity"    "Temperature"
## [6] "GrowthRate"

Okay, let’s take a look at this data graphically:

The purpose of this data set was to find the combination of inputs that led the fastest mushroom growth for sale at the farmers’ market.

Let’s look at that.

Here are the conditions where the max growth rate was found:

Species Light Nitrogen Humidity Temperature GrowthRate
P.cornucopiae 20 20 High 20 664.6693 
## [1] 664.6693

Well, which factors are really important for mushroom growth rate?

Here’s a simple model and a list of significant predictors:

## GrowthRate ~ Light + Species + Nitrogen + Humidity + Temperature
## 
## Call:
## glm(formula = GrowthRate ~ Light + Species + Nitrogen + Humidity + 
##     Temperature, data = df)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -112.19   -47.32    -8.48    35.45   418.31  
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        216.0488    46.4242   4.654 5.77e-06 ***
## Light                5.5128     0.6063   9.093  < 2e-16 ***
## SpeciesP.ostreotus -48.3807     9.9005  -4.887 2.03e-06 ***
## Nitrogen            -0.1579     0.3321  -0.476   0.6349    
## HumidityLow        -86.5783     9.9005  -8.745 7.26e-16 ***
## Temperature         -3.8394     1.9801  -1.939   0.0538 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for gaussian family taken to be 5293.069)
## 
##     Null deviance: 2101436  on 215  degrees of freedom
## Residual deviance: 1111544  on 210  degrees of freedom
## AIC: 2472.9
## 
## Number of Fisher Scoring iterations: 2
term estimate std.error statistic p.value
(Intercept) 216.048767 46.424241 4.653792 5.8e-06
Light 5.512764 0.606279 9.092785 0.0e+00
SpeciesP.ostreotus -48.380660 9.900495 -4.886691 2.0e-06
HumidityLow -86.578337 9.900495 -8.744850 0.0e+00

A reduced model, provided by the MASS::StepAIC() function gives us the following model:

## Start:  AIC=2472.91
## GrowthRate ~ Light + Species + Nitrogen + Humidity + Temperature
## 
##               Df Deviance    AIC
## - Nitrogen     1  1112741 2471.2
## <none>            1111544 2472.9
## - Temperature  1  1131445 2474.8
## - Species      1  1237942 2494.2
## - Humidity     1  1516318 2538.0
## - Light        1  1549169 2542.6
## 
## Step:  AIC=2471.15
## GrowthRate ~ Light + Species + Humidity + Temperature
## 
##               Df Deviance    AIC
## <none>            1112741 2471.2
## - Temperature  1  1132641 2473.0
## - Species      1  1239138 2492.4
## - Humidity     1  1517515 2536.2
## - Light        1  1550365 2540.8
## GrowthRate ~ Light + Species + Humidity + Temperature
term estimate std.error statistic p.value
(Intercept) 212.364338 45.6890416 4.648037 0.0000059
Light 5.512764 0.6051661 9.109505 0.0000000
SpeciesP.ostreotus -48.380660 9.8823217 -4.895678 0.0000019
HumidityLow -86.578337 9.8823217 -8.760931 0.0000000
Temperature -3.839376 1.9764643 -1.942547 0.0534016







And now, since it’s a final project, Dr. Zahn wants many pretty pictures: